Improving Quantum Computer Performance Through Noise and Error Suppression
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Software tools for quantum control: Improving quantum computer performance through noise and error suppression Harrison Ball, Michael J. Biercuk,∗ Andre Carvalho, Jiayin Chen, Michael Hush, Leonardo A. De Castro, Li Li, Per J. Liebermann, and Harry J. Slatyer Q-CTRL, Sydney, NSW Australia & Los Angeles, CA USA Claire Edmunds, Virginia Frey, Cornelius Hempel, and Alistair Milne ARC Centre for Engineered Quantum Systems, The University of Sydney, NSW Australia (Dated: July 4, 2020) Effectively manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise critically limits the performance and capabilities of today's so-called noisy intermediate-scale quan- tum (NISQ) devices, as well as any future quantum computing technologies. Fortunately, quantum control enables efficient execution of quantum logic operations and quantum algorithms with built- in robustness to errors, and without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in quantum comput- ing research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of python-based classical software tools for creating and deploying op- timized quantum control solutions at various layers of the quantum computing software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of central product features including a flexible optimization toolkit, engineering-inspired filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions derived from these tools in real experimental settings using both trapped-ion and superconducting quantum computer hardware. CONTENTS C. Flexible optimization tools for quantum control 12 I. Introduction2 1. Flexible optimizer framework 12 2. Flexible optimizer features 13 II. Software architecture and integrations4 3. Optimizer performance benchmarking 16 A. Cloud-compute architecture4 D. Time-domain simulation tools for realistic B. Package overview4 hardware error processes 16 C. Compatibility with other programming 1. Technical details of simulation languages6 functionality 17 D. Integration with quantum hardware6 2. Simulation example 19 E. Hardware characterization 19 III. Technical functionality overview8 1. Noise spectral estimation 19 A. General quantum-control setting8 1. Optimal quantum control8 2. Hamiltonian parameter estimation 24 2. Robust quantum control9 3. Controllability9 IV. Quantum control case studies 26 B. Performance evaluation for arbitrary A. Open-loop control benefits demonstrated in controls 10 trapped-ion QCs 26 1. Modelling noise and error in D-dimensional B. Simultaneous leakage and noise-robust systems 10 controls for superconducting circuits 28 2. Multi-dimensional filter functions in the C. Robust control for parametrically-driven frequency domain 11 superconducting entangling gates 29 D. Experimental noise characterization of multiqubit circuits on an IBM cloud QC 32 E. Crosstalk-resistant circuit compilation 34 ∗ Also ARC Centre for Engineered Quantum Systems, The Uni- versity of Sydney, NSW Australia V. Conclusion and outlook 37 2 Acknowledgements 37 One of the earliest software methodologies proposed for quantum computing described a 4-phase design flow [8], A. Technical definitions 39 transforming high-level algorithms to mid-level represen- 1. Frobenius inner product and Frobenius norm 39 tations such as QASM (quantum assembly language), ul- 2. Fourier transform 39 timately to be compiled down to device-specific instruc- 3. Power spectral density 39 tions sent to the quantum hardware. Later work out- lined a more detailed layered architecture [9] including a B. Formal definition of the control Hamiltonian 41 pipelined control cycle from the application layer down 1. Generalized formalism 41 to the physical hardware layer, with mid-tier processes 2. Control solutions 41 such as QEC in between. 3. Control segments 42 Since then various QC programming languages, sim- 4. Generic shaped control segments 42 ulators, and compilers have been devised. Starting at 5. Control coordinates 43 the highest levels of the stack, freely-available examples include Quipper [10], a quantum program compiler im- C. Derivation of multidimensional filter functions 45 plemented in Haskell, the LIQUi simulator [11] writ- 1. Magnus expansion 45 ten in F#, and the ScaffCC compilerji [12] designed for 2. Leading order robustness infidelity in terms of a C-style language, which compiles gate sets in QASM filter functions 45 and supports program analysis and low-level optimiza- tions. Further down the stack, efficient scheduling ar- D. Optimization benchmarking 47 chitectures with reduced communication overheads and 1. Optimization tools 47 increased parallelism have been proposed to accommo- 2. Software and hardware versions 47 date the relatively short lifetimes of quantum information 3. Physical systems 47 in quantum hardware [13{15]. Other compiler perfor- a. Single controllable qubit in four-qubit mance gains have been identified by considering device- space 48 specific optimizations, gate set choices and communica- b. Linear array of Rydberg atoms 48 tion topologies [16]. E. Methods for experimental demonstrations of More recently a variety of Python-based languages quantum-control benefits 49 have been developed providing greater integration and 1. Quasi-static error robustness 49 functionality across various abstraction layers. Pro- 2. Suppression of time-varying noise 49 jectQ [17{20] is a toolflow to optimize, simulate and com- 3. Error homogenization characterized via pile quantum programs for different hardware backends. 10-qubit parallel randomized benchmarking 50 Qiskit [2, 21] is a general-purpose compiler framework 4. Mølmer-Sørensen drift measurements 50 generating OpenQASM [22], the language used to cre- ate and compile quantum programs on IBM's Quantum F. Visualizations of noise and control in quantum Experience [23]. pyQuil [4, 24, 25] generates Quil [24], circuits 51 the compiler language used for the Rigetti Computing system. Cirq [5] is Google's software library for writing, References 52 optimizing and running quantum circuits on hardware backends or simulators. Nonetheless, the central impediment to realizing prac- I. INTRODUCTION tical, functional machines in the NISQ-era and beyond remains the influence of noise and error in quantum hard- The emergence of commercially-available quantum ware itself, despite these various advances in quantum computing (QC) hardware at the scale of a few tens of software development. Electromagnetic noise in its vari- qubits has led to an explosion of interest in NISQ (noisy ous forms diminishes coherent lifetimes through the pro- intermediate scalable quantum) devices [1]. There are cess of decoherence, and reduces the fidelity of quan- even now several software stacks allowing end-users and tum logic operations when imperfect quantum devices software developers to explore quantum computing over are manipulated by faulty classical hardware. This crit- the cloud [2{5]. Commensurate with this growth in pro- ically limits the range of useful computations achievable gramming frameworks has been a expansion of efforts on quantum hardware, measured e.g. by circuit depth focused on application mapping and algorithmic devel- or quantum volume [26]. Overwhelmingly, the tools and opment to identify applications yielding any commer- frameworks introduced above focus on the design, imple- cially relevant computational advantage [6]. However, as mentation, and optimization of algorithms near the top in conventional software engineering, functionality and of the quantum computing software stack, and do not computational advantage ultimately rests on lower-level directly address this most fundamental challenge in the abstractions deeper in the computational stack such as field. compilers, and more fundamentally, on hardware device Developing techniques that improve the robustness of performance [7]. quantum hardware against noise and error is critical 3 for pursuing commercially-viable applications. One ap- 1 To advance the performance of real quantum hard- proach to this problem comes through the implemen- ware by delivering optimized control strategies. tation of low-level error-suppression strategies derived More concretely, to enable efficient characterization from the field of quantum control [27{36]. This disci- of error sources, identify and exploit system con- pline draws insights from classical control engineering - trollability, and generate instructions for real hard- frequently associated with the stabilization of unstable ware to suppress the influence of noise and imper- hardware - though successful translation to the quan- fection at the device level. tum domain requires